In this handout, we investigate an alternative way of defining the number e, as the base of the exponential function which is its own derivative. This Desmos graph lets you experiment with different bases of an exponential function, and observe the connection between the exponential function and its derivative.

# Tag: Ch 2

## Implicit Differentiation (2.4)

These notes contain a summary of the important ideas behind implicit differentiation, its connection to the Chain Rule, and how it may be used to find tangent lines to general equations. You can use this Desmos graph to look at the graphs produced by various equations, as well as to check that your answers to…

## Interlude 1 – Newton’s Method

The handout below contains a summary of the important points about Newton’s Method, as well as introduces the Bisection Method for comparison. There are some exercises at the end for you to test your understanding of some of the important ideas. This Desmos graph gives a visual representation of what is going on during each…

## Linear approximations and their derivatives (2.2)

This graph shows how we can make an approximation to the graph of a function using a piecewise function where each piece is a secant line. For this piecewise function — since lines are easy to deal with — we can compute the piecewise derivative and see how this compares with the graph of the…

## Definition of the derivative (2.2)

This Desmos graph shows how the derivative represents the slope of the tangent line to the graph, and can be calculated as the limit of the slopes of secant lines. In the same way that the slope of a secant line represents an “average rate of change”, the slope of the tangent line represents an…

## Derivative Rules Handout

The above PDF handout has a comprehensive list of the derivatives of the essential elementary functions, as well as the rules, from which the derivative of any elementary function can be calculated by hand. Although we will derive almost all of these statements in class, they are – perhaps more than anything else in the…